Why is electricity so sporadic in it’s movement, when solids, liquids, and gasses, are usually straightforward? Basically Newton’s second law states an object will remain in the same trajectory unless acted on by another force. what forces are acting upon an electric arc when it makes a jump between wires? or when it leaves a tesla coil? why isn’t the electric arc in a mostly straight line?
 A: From a classical perspective, the force on a particle with electric charge is
$$
\vec{F} = q\vec{E} + q\vec{v} \times \vec{B}
$$
for chare $q$, electric field $\vec{E}$, and magnetic field $\vec{B}$.  Anything large enough to not need quantum explanations will in essence come down to that, where that force is the same $m\vec{a}$ force from Newton's laws. For reference, the above equation is called the Lorentz force. It is the fundamental force equation for classical electromagnetism. The fundamental equations for the fields themselves, which are needed to calculate the force, are Maxwell's equations.
Something like a spark is actually a bit complex. Basically, it occurs when the field gets so large that some of the electrons in the molecules of the air are freed. This really requires a quantum explanation, but you can think of an analogy as enough force being provided to a satellite to free it from orbit, where the force would come from the $\vec{E}$ in the above. When this happens, the air becomes conductive rather than resistive as it usually is, so current can flow. The flowing current discharges the separated charge that caused the field in the first place, so the air quickly returns to its normal state. When the charge is replenished, the spark can be made to linger, as some demonstration toys do.
The path that it follows is extremely chaotic because where the air ionizes is chaotic. The electrons have very low mass, so the mass time acceleration aspect of Newton's law is unimportant to the process. In fact, in virtually all of circuit analysis one does in electrical engineering, the mass and acceleration of the electrons are completely ignored. They are assumed to come to their steady state drift speed immediately. This is because those drift speeds turn out to be low (low enough that it would probably surprise you), and their random motions of the orbital are high (high enough that it would also probably surprise you).
For reference, electrons in atoms usually have speeds around a million meters per second, while the drift speed in currents is quoted in millimeters or centimeters per minute. This is why circuit analysis can approximate electric particles as having no mass and no acceleration and also why we can see such spectacular displays of chaos in sparking.
Addendum
A commenter below pointed out the comparison between a spark in an air gap and the current in a vacuum tube. You are probably more familiar with air gap sparks, as tubes have been almost completely deprecated from electronics, but you can look them up on the internet, or if you play guitar you may have a tube amplifier. Anyway, the current across a vacuum tube is steady and even controllable. It is in many ways related to the flow in an air gap spark, but completely different in character.
